Trigonometry Examples

$\tan (2.5) (18 + x) = \tan (10) x$

Step 1

For the two functions to be equal, the arguments of each must be equal.

$2.5 = 10$

Step 2

Since $2.5 \neq 10$ , there are no solutions.

No solution

Step 3

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from $π$ to find the solution in the fourth quadrant.

$2.5 = π + 10$

Step 4

Subtract $2 π$ from $π + 10$ .

$2.5 = π + 10 - 2 π$

Step 5

The resulting angle of $10 - π$ is positive, less than $2 π$ , and coterminal with $π + 10$ .

$2.5 = 10 - π$

Step 6

Subtract $2 π$ from $10 - π$ .

$2.5 = 10 - π - 2 π$

Step 7

The resulting angle of $10 - 3 π$ is positive, less than $2 π$ , and coterminal with $π + 10$ .

$2.5 = 10 - 3 π$

Step 8

Solve for $x$ .

Tap for more steps...

Step 8.1

Simplify $10 - 3 \cdot 3.14159265$ .

Tap for more steps...

Step 8.1.1

Multiply $- 3$ by $3.14159265$ .

$2.5 = 10 - 9.42477796$

Step 8.1.2

Subtract $9.42477796$ from $10$ .

$2.5 = 0.57522203$

Step 8.2

Since $2.5 \neq 0.57522203$ , there are no solutions.

No solution